Answer the following questions. Show all of your calculations and label all parts of your graph.
1. Moe owns a restaurant that serves slabs of BBQ ribs. The size of his kitchen and the number of BBQ grills are fixed. Moe can vary the quantity of slabs by changing the number of workers he employs. Each worker earns $10/hr. and the fixed cost is $20. He observes the following relationship between the number of employees and the quantity of slabs produced:
Number of workers Quantity
(slabs per hour) Marginal Product Cost of Workers per hr. Total Cost
0 0
1 25
2 45
3 60
4 70
5 75
a. Fill in the rest of the table.
b. Graph the production function with Number of Workers on the horizontal axis and Quantity of Output on the vertical axis.
c. Does Moe’s production function exhibit diminishing marginal product of labor? Explain.
2. Lauren’s Nail Salon (a perfectly competitive firm) faces costs of production as follows:
Q clients per week Total Revenue Total Cost Variable Cost Average Variable Cost Average Total Cost Marginal Revenue Marginal Cost Profit
0 $0 $100 $0
10 120 150 50
20 240 230 130
30 360 330 230
40 480 450 350
50 600 600 500
60 720 800 700
a. What are Lauren’s fixed costs?
b. Fill in the rest of the table
c. What is the profit-maximizing level of output?
d. Graph MC, AVC, ATC, and MR. Shade in the area that is her profit.
e. At what price will Lauren close her salon and exit the market?
3. A pharmaceutical company owns the patent to produce a drug that cures Alzheimer’s disease. The following equations describe the monopolist’s demand, total revenue, marginal revenue, total cost and marginal cost:
Demand: P = 300 – 10Q
Total Revenue: TR = 300Q – 10Q^2
Marginal Revenue: MR = 300 – 20Q
Total Cost: TC = 30 + 60Q + 5Q^2
Marginal Cost: MC = 60 + 10Q
Where Q is the quantity of bottles sold (in millions) and P is the price in US dollars.
a. Find the price and quantity that maximize the company’s profit.
b. What is the pharmaceutical company’s profit?
c. Find the price and quantity that would maximize social welfare.
4. A tech company created a new tutoring app. It will cost them $1 each time the app is downloaded on iTunes. There are no fixed costs. The marketing department determines that the demand for the app is as follows:
Price Quantity TR MR Profit
$8 $0
7 10,000
6 15,000
5 20,000
4 25,000
3 30,000
2 35,000
1 40,000
a. Find total revenue and marginal revenue.
b. Graph Demand, MR, and MC. Shade in the deadweight loss.
c. What quantity of apps would maximize profits and what would the price be? What is the profit?
d. Suppose the tech company wanted to maximize economic welfare. What price would they charge and how much profit would they make at this price.